Cwikel's estimates in the form stated above were conjectured by Simon [1]}. He pointed out that combining them with the Birman-Schwinger principle [2]}, [3]} would give an upper-bound for the number of negative eigenvalues (i.e., the number of bound states) of Schrödinger operators \(\Delta +V\)  with \(V\in L_{\frac{n}{2}}(\mathbb {R}^n)\) , \(n\ge 3\) . Namely, there exists a constant \(C_n>0\)  depending only on \(n\)  such that
\(N^{-}(\Delta +V) \le C_n\int |V_{-}(x)|^{\frac{n}{2}}dx,\) 
